2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74700Let A \subseteq [1,..,N]^2 be a set of cardinality at least N^2/(log log N)^c, where c>0 is an absolute constant. We prove that A contains a triple {(k,m), (k+d,m), (k,m+d)}, where d>0. This theorem is a two-dimensional generalization of Szemeredi's theorem on arithmetic progression.51 pagesNumber TheoryDynamical Systemstext